What you are asking in the title of your questions and what you are asking in the body of the question are fundamentally different. Asian eyelid surgery generally implies creating a double fold where one did not exist before. Clearly your situation is that you have already had an Asian eyelid surgery and your surgeon has left you with a fold that is too high. Generally I find that many of these situations are further complicated by the fact that the eyelid platform...
Creating a different position for the upper eye lid involves sutures to adjust where very small layers of tissue connect in your eyelid. It is somewhat complex and choose a surgeon familiar with asian eyelid surgery specifically.
One can create, lower and modify the fold in the upper lid without taking any skin. This should be determined by the surgeon at the time of surgery.
As for the details of the surgery , this is a very complex surgery